...the mid-points of the sides BC, CA, AB of the triangle ABC, show that 4. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. ©amfcrtoge : PRINTED BY JOHN CLAY, MA AT THE UNIVERSITY PRESS Mathematics,...

...having each of the base angles double of the vertical angle. 4. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 5. If the base and vertical angle of a triangle are given, prove the locus...

...Y^*. Similarly, for CG = AG = BG, for an equilateral triangle, Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. AB Ideas: (i) Sum of squares suggests Pythagoras' or Apollonius' Theorem....

...constant. .: locus of A is a circle whose centre is the mid. pt. of BC. 1 61 , 3. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Let ABCD be a grain, whose diagonals bisect each other at O (91,1). Now sqs...

...its locus is a circle, having for centre the mid-point of AB. tEx. 1142. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. tEx. 1143. In any quadrilateral the sum of the squares on the four sides...